Noninvasive high-resolution depth-resolved measurement of corneal biomechanics is of great clinical significance for improving the diagnosis and optimizing the treatment of various degenerated ocular diseases. Here, we report a micro-scale optical coherence elastography (OCE) method that enables noncontact assessment of the depthwise elasticity distribution in the cornea. The OCE system combines a focused air-puff device with phase-sensitive optical coherence tomography (OCT). Low-pressure short-duration air stream is used to load the cornea with the localized displacement at micron level. The phase-resolved OCT detection with nano-scale sensitivity probes the induced corneal deformation at various locations within a scanning line, providing the ultra-fast imaging of the corneal lamb wave propagation. With spectral analysis, the amplitude spectra and the phase spectra are available for the estimation of the frequency range of the lamb wave and the quantification of the wave propagation, respectively. Curved propagation paths following the top and bottom corneal boundaries are selected inside the cornea for measuring the phase velocity of the lamb wave at the major frequency components over the whole depths. Our pilot experiments on ex vivo rabbit eyes indicate the distinct stiffness of different layers in the cornea, including the epithelium, the anterior stroma, the posterior stroma, and the innermost region, which demonstrates the feasibility of this micro-scale OCE method for noncontact depth-resolved corneal elastography. Also, the quantification of the lamb wave dispersion in the cornea could lead to the measurement of the elastic modulus, suggesting the potential of this method for quantitative monitoring of the corneal biomechanics.